可数簇全拟- Φ -渐近非扩张映象和广义混合平衡问题以及极大单调算子的收缩投影迭代算法

数学物理学报 ›› 2014, Vol. 34 ›› Issue (2): 283-302.

可数簇全拟- Φ -渐近非扩张映象和广义混合平衡问题以及极大单调算子的收缩投影迭代算法

朱浸华

宜宾学院数学学院四川宜宾644000

收稿日期:2011-11-09 修回日期:2013-05-06 出版日期:2014-04-25 发布日期:2014-04-25
基金资助:
四川省科技厅项目(2012JYZ011)、教育厅重点项目(13ZA0199)和四川省教育厅资助科研项目(14ZA0271)资助.

Hybrid Shrinking Projection Method for a Countable Family of Total Quasi-Φ-Asymptotically Nonexpansive Mappings, a Generalized Mixed Equilibrium Problem and a Maximal Monotone Operator

ZHU Jin-Hua

Department of Mathematics Yibin |University, Sichuan Yibin 644000

Received:2011-11-09 Revised:2013-05-06 Online:2014-04-25 Published:2014-04-25
Supported by:
四川省科技厅项目(2012JYZ011)、教育厅重点项目(13ZA0199)和四川省教育厅资助科研项目(14ZA0271)资助.

摘要/Abstract

摘要：

先介绍全拟- Φ -渐近非扩张映象的概念,然后在具有Kadec-Klee性质的一致光滑、严格凸的Banach空间的框架下,利用混合收缩投影的迭代算法, 用以寻求广义混合平衡问题的解集GMEP,可数簇全拟- Φ -渐近非扩张映象的不动点集∩^∞_i=1F(S_i)和极大单调算子的零点集T^-10的公共元.在适当的条件下, 证明了逼近于这一公共元的强收敛定理. 推广和改进了一些最新结果.

关键词: 广义混合平衡问题, 全拟- Φ -渐近非扩张映象, 拟- Φ -渐近非扩张映象, 拟- Φ -非扩张映象, 混合收缩投影, &beta, -逆强单调映象, 极大单调算子

Abstract:

The purpose of this paper is first to introduce the concept of total quasi-Φ-asympto- tically nonexpansive mapping and then consider a hybrid shrinking projection method for finding a common element of the set GMEP of solutions of a generalized mixed equilibrium problem, the set ∩^∞_i=1F(S_i) of common fixed points of a countable family of total quasi-Φ-asymptotically nonexpansive mappings {S_i}^∞_i=1 and the set T^-10 of zeros of a maximal monotone operator T in a
uniformly smooth and strictly convex Banach space with Kadec-Klee property. It is proven that under appropriate conditions, the sequence generated by the hybrid shrinking projection method, converges strongly to some point in GMEP ∩T^-10 ∩(∩^∞_i=1F(S_i)). This new result represents the improvement, complement and development of the previously known ones in the literature.

Key words: Generalized mixed equilibrium problem, Total quasi-Φ-asymptotically nonexpansive mapping, Quasi-Φ-asymptotically nonexpansive mapping, Quasi-Φ-nonexpansive mapping, Hybrid shrinking projection, β-Inverse strongly monotone mapping, Maximal monotone operator

中图分类号:

47H06

朱浸华. 可数簇全拟- Φ -渐近非扩张映象和广义混合平衡问题以及极大单调算子的收缩投影迭代算法[J]. 数学物理学报, 2014, 34(2): 283-302.

ZHU Jin-Hua. Hybrid Shrinking Projection Method for a Countable Family of Total Quasi-Φ-Asymptotically Nonexpansive Mappings, a Generalized Mixed Equilibrium Problem and a Maximal Monotone Operator[J]. Acta mathematica scientia,Series A, 2014, 34(2): 283-302.

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